Possibly, though they may take issue with the anesthetic. Due to a chicken's faster metabolism, respiratory rate, etc, it's hard to get the dosage right with a lot of the more conventional drugs, and with the rabies risk, the dentist would really not want it to wake up and struggle. In cases like this, most dentists prefer a very old-fashioned anesthetic - an ax. Knock's 'em right out!

Of course, it is a bit hard to wake them up when the procedure is finished . . . .

Possibly, though they may take issue with the anesthetic. Due to a chicken's faster metabolism, respiratory rate, etc, it's hard to get the dosage right with a lot of the more conventional drugs, and with the rabies risk, the dentist would really not want it to wake up and struggle. In cases like this, most dentists prefer a very old-fashioned anesthetic - an ax. Knock's 'em right out!

Of course, it is a bit hard to wake them up when the procedure is finished . . . .

I think you are missing an important part of this equation.....rather than focusing on the abscess and the possibility of rabies as a result, you need to find out what has happened in the chick's environment to cause the issue in the first place. Otherwise you are looking at the possibility of all of the chicks having the same problem. So you'll need to ask yourself a few questions.

What size grit do they get? If the grit is too large, they can't chew it down to a more manageable size. It could even be that what you think is an abscess is actually a bit of grit lodged between two teeth, sort of like when a popcorn hull jams itself between your teeth and gums. If it's jammed in there good, it would be like splinter, swelling and just getting more and more painful. I'd open the chick's mouth and use a toothpick to see if you can dislodge the grit piece, if that's what you find.

Are you adding a little Listerine to their water? Clean gums mean clean teeth. Of course, that won't help the one that is suffering now. You might try holding it carefully, putting a couple of drops of Listerine directly into the mouth (avoid letting it run down either of the holes at the back of the throat) and then hold it by it's little wings and give it a good shake. Since chickens can't gargle like we can, that's as close to mouthwashing action as you're likely to get. It may even serve to dislodge any offending bits of whatever it has caught in it's teeth. Take the opportunity, while you are already holding it and have done the gargling thing, to use a toothpick and carefully clean between each tooth. If the mouth stinks, it's an abscess. If the chick bites, it's mad at you.

What kind of treats do you feed? You know that chicks are even more sensitive to sweets than 3 year old humans because their teeth are so much smaller and close together. Cut back on the sugary treats. They'll be mad and maybe throw a couple of temper tantrums....but they'll get over it.

As far as the rabies threat, you can eliminate that by removing the heat lamp. Rabies needs constant warm temperatures to thrive. So turning off the heat lamp and feeding your chicks some ice cubes will alleviate the swelling and pain and also kill any rabies germs that are hiding in the abscess. You may want to vaccinate the other chicks against rabies first though, so if any of the germs scurry out to get away from the cold and jump into a warmer chick's mouth, they can't multiply.